Systemic Risk and the Refinancing Ratchet Effect

Journal of Financial Economics 108 (2013) 29–45

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Systemic risk and the reﬁnancing ratchet effect$

Amir E. Khandani a,c, Andrew W. Lo b,c,d,n, Robert C. Merton b a Morgan Stanley, New York, United States b MIT Sloan School of Management, 100 Main Street, E62-618, Cambridge, MA 02142, United States c Laboratory for Financial Engineering, MIT Sloan School of Management, United States d AlphaSimplex Group, LLC, United States article info abstract

Article history: The combination of rising home prices, declining interest rates, and near-frictionless Received 13 June 2010 refinancing opportunities can create unintentional synchronization of homeowner leverage, Received in revised form leading to a ‘‘ratchet’’ effect on leverage because homes are indivisible and owner-occupants 7 May 2012 cannot raise equity to reduce leverage when home prices fall. Our simulation of the U.S. Accepted 16 May 2012 housing market yields potential losses of $1.7 trillion from June 2006 to December 2008 Available online 20 November 2012 with cash-out refinancing vs. only $330 billion in the absence of cash-out refinancing. JEL classification: The refinancing ratchet effect is a new type of systemic risk in the financial system and does G01 not rely on any dysfunctional behaviors. G13 & 2012 Elsevier B.V. All rights reserved. G18 G21 E17 R28

Keywords: Systemic risk Financial crisis Household ﬁnance Real estate Subprime mortgage

1. Introduction mainly by the value of the underlying real estate. This feature makes the market value of the collateral very important in Home mortgage loans—one of the most widely used measuring the risk of a mortgage.1 To reduce the risk of financial products by U.S. consumers—are collateralized default, mortgage lenders usually ask for a down payment of 10–20% of the value of the home from the borrower, creating an ‘‘equity buffer’’ that absorbs the first losses from home $ The views and opinions expressed in this article are those of the price declines. Any event or action that reduces the value of authors only, and do not necessarily represent the views and opinions of AlphaSimplex Group, Morgan Stanley, MIT, any of their affiliates and this buffer, e.g., an equity extraction or a drop in home employees, or any of the individuals acknowledged below. We thank Jim values, increases the risk to the lending institution. Kennedy for sharing his data and Terry Belton, Vineer Bhansali, Peter A number of secular trends over the last two decades, Carr, Conan Crum, Jayna Cummings, Arnout Eikeboom, David Geltner, including the increased efficiency of the refinancing Will Goetzmann, Jacob Goldfield, Ben Golub, Matt Jozoff, Jim Kennedy, Atif Mian, Amir Sufi, Bill Wheaton, Matt Zames, and participants at the process and the growth of the refinancing business, have Market Design and Structure Workshop at the Santa Fe Institute, 2010 made it much easier for homeowners to refinance their Western Finance Association Annual Meeting, and 2010 Bank Structure Conference at the Chicago Fed for helpful comments and discussion. Research support from the MIT Laboratory for Financial Engineering is gratefully acknowledged. 1 See, for example, Danis and Pennington-Cross (2005), Downing, n Corresponding author at: MIT Sloan School of Management, 100 Stanton, and Wallace (2005), Gerardi, Shapiro, and Willen (2007), Doms, Main Street, E62-618, Cambridge, MA 02142, United States. Furlong, and Krainer (2007), Bajari, Chu, and Park (2008), Bhardwaj and E-mail address: [email protected] (A.W. Lo). Sengupta (2008a), and Gerardi, Lehnert, Sherlund, and Willen (2008).

0304-405X/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jfineco.2012.10.007 30 A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45 mortgages to take advantage of declining interest rates, the collateral. Furthermore, the occupant is almost always increasing housing prices, or both. Consequences of these the sole equityholder in an owner-occupied residential trends have been documented by Greenspan and Kennedy property, and moral hazard concerns preclude the owner (2008, p. 120), who observe, ‘‘since the mid-1980s, mort- from reducing leverage by raising incremental capital via gage debt has grown more rapidly than home values, issuing equity to others. resulting in a decline in housing wealth as a share of the These two special features of residential real estate may value of homes.’’ They attribute most of this effect to be viewed as market frictions or institutional rigidities that discretionary equity extractions via home sales, ‘‘cash- create an important asymmetry in the housing market which out’’ refinancing (where the homeowner receives cash does not exist in most financial markets. While a leveraged after the refinancing), and home-equity loans. investor may decide not to incrementally deleverage as In this paper, we focus on a previously unstudied prices decline due to optimistic expectations of a price dimension of risk in the mortgage market: the interplay reversal, indivisibility and occupant-ownership make incre- among the growth of the refinancing business, the decline mental deleveraging impossible, even for those who wish to in interest rates, and the appreciation of property values. reduce their exposure to real estate. Therefore, the only Each of these three trends is systemically neutral or option available to homeowners in a declining market is to positive when considered in isolation, but when they sell their homes, recognize their capital losses, and move into occur simultaneously, the results can be explosive. less expensive properties that satisfy their desired LTV ratio. We argue that during periods of rising home prices, falling The enormous costs—both financial and psychological—of interest rates, and increasingly competitive and efficient such a transaction make it a highly impractical and implau- refinancing markets, cash-out refinancing is like a ratchet. sible response to addressing the issue raised in this paper. It incrementally increases homeowner leverage as real- We propose to gauge the magnitude of the potential risk estate values appreciate without the ability to symme- caused by the refinancing ratchet effect by creating a trically decrease leverage by increments as real-estate numerical simulation of the U.S. housing and mortgage values decline. This self-synchronizing ‘‘ratchet effect’’ markets. By calibrating our simulation to the existing stock can create significant systemic risk in an otherwise of real estate, and by specifying reasonable behavioral geographically and temporally diverse pool of mortgages. rules for the typical homeowner’s equity extraction The potential magnitude of the risk created due to the decision—which satisfy common standards of prudence refinancing ratchet effect is most clearly illustrated though a and good lending practices in the U.S.—our simulation can hypothetical scenario in which all homeowners decide to match some of the major trends in this market over the past keep their leverage at a level generally associated with decade. Based on the calibrated simulation and using a extreme prudence and good lending practices, for example, standard derivatives-pricing model, we construct an estimate a loan-to-value (LTV) of 80% for a conventional fully amortiz- of losses absorbed by mortgage lenders—banks, asset man- ing 30-year fixed-rate mortgage. Suppose the refinancing agement firms, and government-sponsored enterprises market is so competitive, i.e., refinancing costs are so low and (GSEs)—from the decline in real-estate prices and compare capital is so plentiful, that homeowners are able to extract these estimates with the scenario of no equity extractions any equity above the minimum each month. In such an over the same period. Our simulation yields an approximate extreme case, cash-out refinancing has the same effect as if loss of $1.7 trillion from the housing-market decline since all mortgages were re-originated at the peak of the housing June 2006 compared to a loss of $330 billion if no equity had market. When home prices fall, as they must eventually, the been extracted from U.S. residential real estate during the ratchet ‘‘locks’’ because homeowners cannot easily unwind boom. their real-estate positions and incrementally deleverage due Of course, a simple response to the refinancing ratchet to indivisibility and illiquidity. The unintentional synchroni- effect might be to eliminate non-recourse mortgages. If all zation of leverage during the market’s rise naturally leads to mortgages were recourse loans and borrowers had uncor- an apparent shift in regime during the market’s decline, in related sources of income, their income streams would which historically uncorrelated defaults now become highly create an extra level of protection for lenders and, there- correlated. fore, distribute the risk in the mortgage system between Indivisibility and occupant-ownership of residential real- lenders and borrowers more evenly. Instead, current legal estate are two special characteristics of this asset class procedures for foreclosure and obtaining deficiency judg- that make addressing this issue particularly challenging. ments are complex and vary greatly from state to state. The impact of indivisibility can be crystallized by comparing As discussed by Ghent and Kudlyak (2009, Table 1), while an investment in residential real estate with a leveraged home mortgages are explicitly non-recourse in only 11 investment in a typical exchange-traded instrument such as states, in certain populous states with recourse such as shares of common stock. While the latter is subject to both Florida and Texas, generous homestead-exemption laws an initial margin requirement as well as a maintenance can make it virtually impossible for lenders to collect on margin requirement, home mortgages only have a home- deficiency judgments because borrowers can easily shield owner equity requirement that plays a role similar to that of their assets. Nevertheless, the risks and potential losses an initial margin. It is hard to imagine that homeowners calculated according to the framework proposed in this would willingly finance large capital purchases using short- paper must be borne by some combination of borrowers term debt like margin accounts, and long-term debt may and lenders; from our systemic-risk perspective, the precise have become the standard method for financing home combination is of less consequence than the aggregate purchases precisely because of the indivisible nature of magnitude. A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45 31

While we have attempted to construct as realistic a have focused on the unique interplay between refinancing simulation as possible, we acknowledge at the outset that and systemic risk in the residential mortgage system that our approach is intended to capture ‘‘reduced-form’’ we examine in this paper. relations and is not based on a general-equilibrium model The uncertain durations and credit risk of mortgages— of households and mortgage lenders. Instead of relying on due to prepayment or default by the borrower—make a stylized general-equilibrium model, we adopt a simple their risks different from other fixed-income products. refinancing rule that seems to capture plausible behavior The approach to modeling these risks can be divided into among U.S. homeowners over the recent past. Also, we do two categories: structural and reduced-form. Structural not model the supply of refinancing and the behavior of models focus on the underlying dynamics of the collateral lenders, but rather assume that households can refinance value and the interest rates to arrive at a model of as much as they wish at prevailing historical interest consumer behavior, while reduced-form models take a rates. While the plentiful supply of credit had been close more statistical approach. Kau, Keenan, Muller, and to reality during the decade leading up to the peak of the Epperson (1992, 1995) and Kau and Keenan (1995) housing market in June 2006, our motivation for this provide some early examples of the structural approach assumption is to isolate the impact of the refinancing while Schwartz and Torous (1989), Deng, Quigley, and ratchet effect. Lending behavior undoubtedly contributed Van Order (2000), and Deng and Quigley (2002) take the to the magnitude of the Financial Crisis of 2007–2009, as reduced-form approach in their studies. LaCour-Little did many other factors (see Lo, 2012 for a review of the (2008) provides a recent review of this literature. burgeoning crisis literature). An empirically accurate The earliest structural models adopted simplifying stochastic dynamic general-equilibrium model of the assumptions that yielded elegant closed-form solutions at housing and mortgage markets that endogenizes these the expense of certain stylized facts of the U.S. mortgage factors is a much more challenging undertaking and market that could not be captured by those assumptions. beyond the scope of this paper. For example, consider the decision to default on a mortgage. Our objective is not to explain the crisis, but rather to The value of the underlying real estate is obviously the most show that even in the absence of any dysfunctional important factor in driving this decision. However, while behavior such as excessive risk-taking, fraud, regulatory negative equity may be a necessary condition to trigger forbearance, political intervention, and predatory borrow- default, it is apparently not sufficient (Foote, Gerardi, and ing and lending, large system-wide shocks can occur in Willen, 2008), perhaps due to concerns such as moving the housing and mortgage markets. The refinancing costs, the desire to preserve reputational capital, default ratchet effect is a considerably more subtle and complex penalties, or even sentimental attachment to the home.2 form of systemic risk, arising from the confluence of three Similarly, homeowners seeking to refinance into a lower familiar and individually welfare-improving economic interest-rate mortgage when rates decline may be con- trends coupled with inherent frictions in the housing strained by their financial circumstances or insufficient market. The simplicity of our simulation approach makes amounts of equity in their homes.3 the refinancing ratchet effect more transparent, and the Such complexities make complete modeling of risk in the potential magnitude of its impact suggests that further residential mortgage system challenging. To avoid the possi- attention is warranted. bility that our main message could be lost while dealing with We begin in Section 2 with a brief review of the these complexities, we have adopted a simple yet realistic literature. We outline the design of our simulation and behavioral rule that can be easily understood and allows us describe the results of the calibration exercise in Section 3. to focus on the main subject of our paper. Our approach for We use these results in conjunction with a simple option- evaluating risk and pricing mortgage guarantees uses option- pricing model in Section 4 to estimate the impact of pricing technology that makes the analytical aspects of our mortgage refinancing on the aggregate risk of the U.S. approach closer to the structural models. mortgage market as home prices declined from 2006 to We argue that the increasing familiarity of borrowers 2008. We provide some qualifications for and extensions with the refinancing process; the invention of new mort- of our results in Section 5, and provide conclusions in gage products; and the corresponding institutional, social, Section 6. and political changes over the last decade contributed to an environment fertile for the type of risk that is the focus of 2. Literature review this paper. Other researchers have studied and commented on this topic as well. For example, by comparing the Given the magnitude of the subprime mortgage crisis, refinancing decision of homeowners in the 1980s relative a number of recent papers have attempted to trace its root to the 1990s, Bennett, Peach, and Peristiani (2001) find causes. Dell’Ariccia, Igan, and Laeven (2012), Demyanyk evidence that over time, a combination of technological, and Van Hemert (2011), Bhardwaj and Sengupta (2008b), regulatory, and structural changes has reduced the net Keys, Mukherjee, Seru, and Vig (2008), and Mian and Sufi (2009) are only a few of the examples in this vast and growing literature. While the issues discussed in these 2 Stanton (1995) and Downing, Stanton, and Wallace (2005) incor- papers, such as lax lending standards and the impact of porate some of these effects into their models of mortgage termination. 3 Archer, Ling, and McGill (1997) and Peristiani, Bennett, Peach, and institutional changes like securitization or the expansion Raiff (1997) consider the impact of household financial conditions such of the subprime market, were certainly of primary impor- as income, credit history, and the amount of homeowner’s equity on the tance in causing the recent crisis, none of these papers ability to refinance. 32 A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45 benefit needed to trigger a refinancing decision. They a given month. Therefore, for each complete run of our conjecture that homeowners’ familiarity with the refinan- simulations, we simulate approximately 1.1 million indi- cing process and their increased financial sophistication are vidual paths. For each path, we keep track of home value, possible drivers behind this phenomenon. interest rate, mortgage outstanding, and several option- Two examples of new mortgage products that enabled based risk measures. The information is then aggregated easier refinancing are the ‘‘subprime’’ and ‘‘Alt-A’’ mort- to arrive at system-wide time series of interest such as gages. As Mayer and Pence (2008, p. 1) observe, ‘‘these total mortgage debt outstanding, total equity extracted, new products not only allowed new buyers to access and various option-based risk metrics. credit, but also made it easier for homeowners to refi- We describe the details of our simulation assumptions in nance loans and withdraw cash from houses that had Section 3.1. Our simulations depend on a number of para- appreciated in value.’’ They point out that ‘‘subprime meters and for expositional clarity, we have summarized mortgages are used a bit more for refinancing than home these parameters in Table 1. In particular, the specific rule purchase’’ and ‘‘almost all subprime refinances are cash- that individuals follow in their refinancing decisions is a out refinances’’ (Mayer and Pence, 2008, p. 10). Moreover, critical component of the simulations, and we describe the some of the more exotic products like non- or negative- rule we use in Section 3.2.InSection 3.3,wereportthe amortization mortgages are contractual equivalents to results of our calibration exercise and specify the set of dynamic strategies involving frequent cash-out refinan- parameters to be used throughout the simulations. cing to maintain a desired leverage ratio. These product innovations may have facilitated large-scale equity 3.1. Simulation assumptions extractions by making refinancing significantly easier, 4 cheaper, and virtually automatic. The behavioral and In designing our simulation, we must balance the social aspects of the decision to default on a residential desire for realism against the availability of data and the mortgage is considered by Guiso, Sapienza, and Zingales tractability of the computations required. To that end, we (2009) using surveys of American households in late 2008 make the following assumptions: and early 2009. They find that households who have been exposed to defaults are more willing to default strategi- (A1) Each house is purchased at an initial LTV ratio drawn cally, i.e., to default even though they can afford their from a distribution that is fixed through time and mortgage payments. For example, individuals who know does not have any geographical dependency. someone who defaulted strategically are 82% more likely (A2) All homes are purchased with conventional fixed- to declare their intention to do so. rate mortgages that are non-recourse loans with Perhaps a similar set of forces was at play during the most initial maturity drawn from a distribution that is recent cash-out refinancing boom. Institutional changes, fixed through time and does not have geographical heightened competition, and technological advances made dependency. it easier and cheaper for consumers to engage in mortgage (A3) The market value of homes follows a geometric refinancing, and increased awareness of and familiarity with random walk given by: the refinancing process made it more popular. Even though log P log P ¼ b þN , ð1Þ many homeowners were undoubtedly aware of the potential i,t i,t1 rt it dangers of equity extractions, the fact that many of their where brt is the cross-sectional common factor in neighbors or co-workers were extracting equity from their home price appreciation for all homes in a given homes made it more socially acceptable to do so at the region r and Nit is the idiosyncratic component for height of the housing boom. each home and month. We calibrate brt, r ¼ 1, ...,10, to 10 distinct regional home price indexes and assume 3. Simulating the U.S. mortgage market Nit to be serially uncorrelated normal random variables with a volatility that is constant through time Our main workhorse in this paper is a simulation of and across all regions (see Table 1 for more details). the U.S. residential mortgage system that attempts to (A4) We allow homeowners the possibility of engaging in capture first-order risks in this market. We simulate each ‘‘Cash-out refinancing’’ or ‘‘Rate refinancing’’ in each home from the time it enters into the mortgage system month. and follow it as it ages and its mortgage is fully paid off. (A5) For Cash-out refinancing, we assume that the ith By listing a set of simple and reasonable rules, we try to homeowner’s decision is random with probability calibrate our simulations to match the overall size and REFIi,t which is a function only of the current equity major trends in the U.S. housing and mortgage markets. in the home and the prevailing mortgage rate. To ensure that our simulation is computationally feasible In particular, we assume that the refinancing deci- given the computing power available to us, we simulate sion does not depend on factors such as the price 1,000 paths for homes that enter the mortgage system in and age of the home, or the time elapsed since any previous refinancing. We also assume that the homeowner will refinance into a new loan with 4 Many of these innovations may also have important tax or the initial LTV ratio and maturity specified in transaction-cost benefits to the borrower; hence, they may have been Assumptions (A1) and (A2). demand-driven rather than the result of overly aggressive mortgage lenders. In fact, these products may be essential for achieving optimal (A6) The owners will engage in a Rate refinancing as soon risk-sharing. as mortgage rates have fallen by more than the ‘‘Rate A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45 33

Table 1 Time series data used to calibrate a simulation of the U.S. housing and mortgage markets. See the Appendix for details.

Data item Description

Home price appreciation Prior to 1987, we assume that all homes grow at a rate specified by a single nationwide Home Price Index constructed using data from Robert Shiller prior to 1975Q1 and data from the FHFA for 1975Q4–1986Q4. After 1987, we use the ten individual series from the Standard and Poor’s (S&P)/Case-Shiller Composite-10 Home Price Index to introduce geographical heterogeneity in our simulations New homes entering the The number of new homes entering the mortgage system is calculated using data from the U.S. Census Bureau after mortgage system 1963. We make some adjustments to take into account homes built by owners or by contractors. For years prior to 1963, we use a statistical approach outlined in the Appendix to backfill the data. Post-1987, we use the weights as given by the S&P/Case-Shiller Composite-10 Home Price Index to calculate the number of new homes in each of the ten regions New home purchase price We construct a time series of the average price of new homes using data from the U.S. Census Bureau since 1963. We backfill the data using our Home Price Appreciation index to January 1919. Finally, we use data from the 2007 American Housing Survey to create a distribution with 15 different price levels around the average series Initial loan-to-value ratio We assume that the initial loan-to-value ratios are uniformly distributed between 75% and 95% Initial mortgage maturity Based on the data from the 2007 American Housing Survey, 80% of mortgages are assumed to be 30-year fixed-rate and the remaining 20% are 15-year fixed-rate, all with standard amortization Long-term risk-free rate After February 1977, we use the yield on constant maturity 30-year Treasury bonds. For earlier periods, we use the annual long-term interest rate data collected by Robert Shiller and interpolate it to arrive at monthly series Mortgage rates For 30-year mortgages, we use the data available from Federal Home Loan Mortgage Corporation (Freddie Mac) for periods after April 1971. For earlier periods, we add 150 basis points (bps) to our Long-term risk-free rate and use the resulting time series. 150 bps is selected based on the average difference between these series in the post-1971 period. For 15-year mortgages, we use the data available from Freddie Mac since September 1991. For earlier periods, we subtract 46 bps from the 30-year mortgages to arrive at the 15-year series. 46 bps is the average difference between the two series in the post-1991 period Home price volatility Determines the volatility of individual home values around the mean given by the Home Price Index. The observed volatility of national home price indexes masks much of the idiosyncratic volatility of individual home prices. Fortunately, an estimate for the volatility of individual homes is produced in the process of estimating the repeated-sales index. Based on the data available from the FHFA,a we use 8% annual volatility in our study. Since this is central to all of our derivatives-related calculations, we also report results assuming for 6% and 10% annualized volatility Rent yield Determines the service flow, akin to dividend payouts from common stock, from home ownership. This parameter affects derivatives-related calculations. Motivated by Himmelberg, Mayer, and Sinai (2005), we use 4% annual yield in the base case, but also report results assuming values of 3% and 5% rent yield Rates refinance threshold Determines the minimum drop in mortgage rates needed to trigger a rates refinancing. We set this threshold to 2% in all simulations, but the simulation results are not very sensitive to this value LTV refinance threshold Determines the maximum level of LTV, beyond which homeowners cannot engage in cash-out refinancing. Given our assumption that the initial LTV is distributed between 75% and 95%, we set this parameter to 75% Prepayment probability Determines the propensity of individuals to pre-pay their mortgage. We use a value of 1 bps per month, but the simulation results are not very sensitive to this value

a See http://www.fhfa.gov/Default.aspx?Page=87. The relevant data are given in the sections ‘‘Purchase Only Indexes Volatility’’ and ‘‘All-Transactions Indexes Volatility.’’

refinance threshold’’ (RRT) from the existing mortgage change throughout time and all mortgages were standard rate. The new mortgage is assumed to have the same and fully amortizing. Of course, in the years leading up to maturity as the existing mortgage, and the principal of the peak of the housing market in 2006, considerably more the new mortgage is equal to the remaining value of aggressive and exotic loans were made, including the now- the existing mortgage. Therefore, the homeowner will infamous NINJA (no income, no job or assets) mortgages and save in monthly payments due to the lower mortgage many others with embedded options. Assumptions (A1) and rate, but no equity is extracted. (A2) are motivated by our desire for simplicity; we also wish (A7) Homeowners’ refinancing decisions are random and to err on the side of caution with respect to default-related independent of each other, apart from the dependence loss implications wherever possible. explicitly parameterized in the refinancing rule. Assuming that mortgages are non-recourse loans (A8) Once fully paid for, a home will not re-enter the greatly simplifies our simulations because we do not need housing market. to model the dynamics of other sources of collateral. (A9) We do not incorporate taxes or transaction costs However, by assuming that lenders have no recourse to explicitly into our simulations. any other sources of collateral, our simulation may yield over-estimates of potential losses, and it may also over- simplify the behavior of borrowers (see Ghent and Given the central role that these assumptions play in our Kudlyak, 2009). To take on the more complex challenge simulations and their interpretation, a few words about of matching the mix of recourse and non-recourse loans their motivation are in order. in the mortgage system in our simulations, we would Assumptions (A1) and (A2) determine the initial leverage require information about the types of recourse that are and type of mortgages we assume for new homeowners. permitted and the practicalities of enforcing deficiency Here, we have assumed the initial LTV distribution did not judgments in each of the 50 states, as well as cross- 34 A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45 sectional and time-series properties of homeowner local, regional, and macroeconomic factors that create income levels, assets, and liabilities. While this task is common drivers in residential real estate. beyond the scope of our current study, it is not insur- Assumptions (A4)–(A6) are simple behavioral rules mountable given sufficient time, resources, and access to meant to encapsulate the economic deliberations of home- financial data at the household level. owners as they decide whether or not to refinance. Accord- Assumption (A3) allows us to calibrate the price ingly, implicit in these rules are many factors that we do not dynamics of our simulated housing stock. We introduce model explicitly, e.g., transactions costs, opportunity costs, geographical heterogeneity in the mean home price homeowner characteristics such as income and risk prefer- appreciation rate, brt, but assume that the volatility of ences, macroeconomic conditions, and social norms. While it the idiosyncratic component is constant and use the may be possible to derive similar rules from first principles estimated volatility as reported by the Federal Housing (e.g., Stanton, 1995), the computational challenges may Finance Agency (FHFA) in our simulations (see Table 1 for outweigh the benefits, especially from the perspective of more details). Once again, these assumptions are meant to producing estimates of potential losses for the aggregate err on the conservative side. For example, it is likely that housing sector. home price volatility spiked in regions with sharp price Assumptions (A5) and (A6) outline the two polar declines, or after national price levels dropped; we ignore opposites of our simulated refinancing activities—(A5) such spikes in our simulations. describes the situation where owners decide to increase The apparent inconsistency between our assumed their mortgage debt to extract equity from their homes dynamics (A3) and the smooth rise and fall in home price while (A6) describes the situation where owners do not indexes deserves further discussion. First, note that our change the size of their mortgage debt but refinance to assumed dynamics are consistent with the standard take advantage of declining interest rates. Clearly, a weighted-repeat-sales index construction methodology number of intermediate cases can be considered, but we (see, for example, Calhoun, 1996). While aggregate home focus only on these two extremes to delineate the price series certainly do not appear to be consistent with boundaries that separate them. geometric Brownian motion—they are far too ‘‘smooth’’—- Implicit in (A4)–(A6) is the assumption that the supply the common component brt does reflect the smoothness of credit to households is infinitely elastic at prevailing induced by aggregation. For our purposes, the volatility of market rates, and it is motivated by our interest in the idiosyncratic term Nit is the key input into determining measuring the impact of household refinancing behavior the value of the embedded put. As noted earlier, this in and of itself. The complexities of consumer credit volatility is calibrated according to FHFA volatility esti- markets warrant a separate simulation study focusing mates.5 Of course, the relative magnitude of the systematic on just those issues. and idiosyncratic volatility in home price returns has Assumption (A7) requires some clarification because important implications for our results. The synchronization the refinancing rules in (A5) and (A6) imply that refinan- of homeowner leverage operates on homes that share a cing decisions are not independent across households. common factor, and the housing and mortgage markets are Assumption (A7) simply states that there are no other most susceptible to the ratchet effect when that common sources of dependence (e.g., peer pressure and social factor has experienced long periods of positive momentum. norms arising from the refinancing activity of neighbors). In a world where home prices contained little or no The only channel through which refinancing decisions are systematic risk, the ratchet effect would be weaker. How- correlated across households in our simulation is through ever, such a world is both counterfactual and difficult to interest rates and home prices via the behavioral rules in reconcile with common intuition regarding the influence of (A5) and (A6). Remarkably, this single source of common- ality is sufficient to generate an enormous amount of synchronized losses when home prices decline. Finally, 5 To the extent that brt induces a smooth time-varying expected Assumption (A8) is motivated primarily by the desire for return, this can be addressed by the mean-reverting diffusion processes simplicity, and can easily be amended to allow fully paid in Lo and Wang (1995). The implications for option-pricing analysis are particularly straightforward (only the drift is affected by mean reversion, houses to re-enter the real-estate market. implying that the option-pricing formula is unchanged but the esti- Ignoring issues such as relocation or renting vs. owning mated volatility must be adjusted for serial correlation). In our analysis, is not likely to affect our estimates of aggregate risk and we use the idiosyncratic volatility of each home as estimated by the losses. For example, consider the case of an individual who FHFA and therefore no adjustment is required. Another extension is to decides to rent after selling for $200,000 a home that was consider price dynamics that reflect the U.S. real-estate ‘‘bubble.’’ However, developing a precise definition of a bubble is not a simple recently purchased for $100,000 with a down payment of task. For example, while some studies concluded that real estate prices $15,000. Assuming a 0% interest rate for simplicity, this were too high in 2004–2006 (Shiller, 2006), other studies came to the fortunate individual has taken $115,000 of equity out of the opposite conclusion (McCarthy and Peach, 2004; Himmelberg, Mayer, housing market. However, the new buyer of this home will and Sinai, 2005). Even ex post, estimating the appropriate ‘‘price correction’’ is not obvious, as Wheaton and Nechayev (2007) illustrate. likely borrow all but 10–20% of the purchase price. For the This lack of consensus underscores the empirical challenges in identify- purpose of measuring aggregate risk, this transaction is ing stable relations between prices and the most obvious fundamentals virtually identical to a cash-out refinancing by the original (in particular, see Gallin, 2004, 2006). But to the extent that a ‘‘bubble’’ homeowner. refers, instead, to an impending tail event, this case can easily be Assumption (A9) is a standard simplification but is not accommodated by assuming a jump component in the stochastic process of the Home Price Index, and then using Merton’s (1976) equivalent to the usual ‘‘perfect markets’’ assumption jump-diffusion option-pricing model to price the embedded put. where taxes and transactions costs are assumed to be A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45 35 zero. In fact, assuming away market frictions may seem intensityðtÞ,’’ is active when the rate on the current particularly incongruous in the context of a simulation of mortgage, MRi,0, is above the prevailing rate of MRt. This refinancing activity, which some consider to be driven second component can be a function of time. In fact, in largely by transactions costs. Assumption (A9) does not some of our simulations we assume that refinancing assert that these frictions do not exist, but merely that we intensity increases through time perhaps due to techno- do not model their impact on behavior explicitly. Instead, logical change, consumer familiarity, or other such fac- our behavioral rules for the homeowner’s refinancing tors. Ultimately, the ability of this model to capture the decision implicitly incorporate these costs into our simu- main drivers of refinancing trends will be judged by lation in a ‘‘reduced-form’’ manner. the success in reproducing the calibration time series. With these assumptions in place, we can now turn to We turn to this issue in the next section. the specific inputs of the simulation. Since our simulations depend on a relatively long list of input parameters 3.3. Calibration exercise and time series, a summary of all of them is provided in Table 1. Due to space limitations, we have relegated more Our goal is to calibrate the parameters of our simula- detailed information to the Appendix. For three of our tion to closely resemble critical aspects of the U.S. parameters—‘‘Rates refinance threshold,’’ ‘‘LTV refinance residential mortgage system as captured by the following threshold,’’ and ‘‘Prepayment probability’’ (see Table 1 for two historical time series: definitions)—we were unable to find appropriate data to calibrate their behavior over time. In lieu of formal 1. Outstanding mortgage volume. We use the value of calibration, we set these parameters to plausible values, residential mortgage liabilities as reported in the and have conducted a series of sensitivity analyses that Federal Reserve Flow of Funds Accounts. These data confirm the robustness of our findings to perturbations are available at a quarterly frequency from 1951Q4 to around these values. 2008Q4, and annually from 1945 to 1951. 2. Equity Extractions. We use the series produced by 3.2. Parameterization of the refinancing probability Greenspan and Kennedy (2005), which is available at a quarterly frequency from 1968Q1 to 2008Q4. The path each home follows is driven by factors such as the evolution of mean home prices, mortgage rates The calibration of our simulation consists of specifying a (MR), and the realization of idiosyncratic home price base refinancing rate and a refinancing intensity function movement around the mean home price, as well as the that can reproduce the above two series as closely as owners’ refinancing decisions as described in Assump- possible. Since the time series used in these calibrations tions (A5) and (A6). The main driver of our simulation are non-stationary, traditional measures such as correlation results is REFI (see Assumption (A5)), which determines i,t and R2 may be misleading indicators of goodness-of-fit. the probability that homeowner i may participate in a A simpler alternative is to compute the mean of the cash-out refinancing in month t. We assume that REFI i,t quarterly absolute deviations between the simulated and has the following functional form: actual series as a percentage of the actual quarterly values: REFI ¼ðLTV 75%Þ½Base refinancing rate i,t i,t o XT 1 9SimulatedtActualt9 þðMRt oMRi,0ÞRefinancing intensityðtÞ: ð2Þ Mean absolute deviation : T Actual k ¼ 1 t Our motivation for selecting this particular character- ð3Þ ization requires some discussion. As noted earlier, our object in this paper is to construct a simple yet realistic We begin with a base refinancing rate of 0.1% per month simulation that matches the size and growth of the U.S. and assume that the refinancing intensity is constant over residential mortgage system and to use that to study the the entire sample period. By varying the level of the potential risk caused by the refinancing ratchet effect refinancing intensity function, we try to achieve a low level alone. This objective reduces the burden on us to have a for the Mean Absolute Deviation (MAD) for both our rule in place that is plausible for the behavior of owners. calibration series. Table 2 contains the MAD results of this The particular characterization proposed here is simple, calibration exercise for three time periods: 1980–2008, yet it has a number of intuitively plausible properties. 1990–2008, and 2000–2008. The results suggest that a First, its assumed form ensures that owners do not refinancing intensity level of 4.00% achieves the lowest level participate in a cash-out refinancing unless they have at of MAD across both calibration reference series during the least 25% equity in their home. Given the assumed 2000–2008 period, which is the most relevant period for our distribution for the initial LTV, this constraint ensures purposes. that individuals participate in cash-out refinancing only Fig. 1 depicts the entire time series produced by our after they have had time to build some equity above their simulations for the combination of input parameters initial equity level. For those owners who satisfy this LTV selected. While our simulations capture the massive constraint, the refinancing intensity has two parts. One growth in the amount of mortgages outstanding and part, given by the ‘‘Base refinancing rate,’’ is constant cumulative equity extractions after 2000 very well, they through time and independent of the rate on the out- fall behind the calibration series between the mid-1980s standing mortgage relative to the prevailing market and the late 1990s. However, since our main focus in this rate. The second component, given by ‘‘Refinancing paper is to evaluate risk in the mortgage system in the 36 A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45

Table 2 Peach, and Peristiani, 2001). The results based on these Summary of Mean Absolute Deviations (MAD), defined in (3), between refinancing rules are provided in the Appendix. the results produced by our simulation approach and the calibration reference series for Total mortgages outstanding and cumulative equity extractions in the U.S. housing market. 4. Options-based risk analysis Cash-out refinancing takes place according to the probabilistic rule given in (2) where the Base refinancing rate is 0.1% per month and the refinancing intensity is constant and given by the first element of each Armed with a properly calibrated simulation of the row. The time series of Total mortgages outstanding is compared with U.S. residential mortgage market, we now turn to asses- the Total mortgage liability series from Flow of Funds Accounts; the time sing the systemic risk posed by the refinancing ratchet series of Cumulative equity extractions is compared with the series effect. Given our assumption that all mortgages in our produced by Greenspan and Kennedy (2005). The MAD is reported for three different time periods to prove additional details about the success simulations are non-recourse loans—collateralized only of the calibration procedure. by the value of the underlying real estate—the homeowner has a guarantee or put option that allows him to MAD of mortgages MAD of cumulative put or ‘‘sell’’ the home to the lender at the remaining outstanding (%) equity extractions (%) value of the loan if the value of the home declines below Uniform 80–08 90–08 00–08 80–08 90–08 00–08 the outstanding mortgage. Such guarantees can be eval- uated using derivatives-pricing theory as described in 2.00% 24.39 23.78 21.82 33.57 32.31 26.82 Merton (1977) and Merton and Bodie (1992), and can be 2.25% 22.78 21.50 18.84 31.00 28.99 22.64 applied to quantify macro-level risks as described in Gray, 2.50% 21.07 19.15 15.88 28.26 25.49 18.42 2.75% 19.78 17.26 13.39 26.16 22.72 14.96 Merton, and Bodie (2006, 2007a,b, 2008) and Gray and 3.00% 18.46 15.44 11.06 24.07 20.07 11.69 Malone (2008). 3.25% 17.54 14.09 9.33 22.71 18.23 9.47 As mortgages are placed in various structured products 3.50% 16.46 12.58 7.42 21.37 16.48 7.75 like collateralized mortgage obligations and then sold and 3.75% 15.72 11.55 6.20 20.52 15.48 7.13 re-sold to banks, asset-management firms, or GSEs (see 4.00% 15.12 10.72 5.51 19.89 14.76 7.22 4.25% 14.58 10.07 5.25 19.28 14.25 7.90 Fig. 3), the ultimate entities exposed to these guarantees 4.50% 14.32 9.74 5.32 19.13 14.15 8.76 may be masked. However, it is clear that all mortgage lenders must, in the aggregate, be holding the guarantees provided to all homeowners. Therefore, we can circumvent the complexities of these intermediate transactions— those in the dotted box of Fig. 3—and use the aggregate years leading up to the Financial Crisis of 2007–2009, the value of the guarantees and their various risk metrics lack of fit in earlier periods is not as problematic. to evaluate the overall risk in the mortgage system. The refinancing intensity levels of 4.00% per month may As discussed earlier, to the extent that some owners may seem excessively high, but note this level is only relevant be liable for the deficiency in their collateral value through for homes that meet both the LTV and the mortgage rate recourse, those owners share some of the burden of the loss conditions in (2). To develop further intuition for this caused by a decline in home prices. Therefore, the economic aspect of our simulation, we computed the fraction of loss and various risk metrics estimated in this section homes in our simulation that meet both conditions in (2). should be viewed as the amount of economic loss or the Fig. 2(a) shows the time series of the percentage of homes risk exposure for the lenders and the subset of borrowers that meet the LTV condition of (2) and Fig. 2(b) provides that are legally responsible via recourse mortgages. the corresponding time series for the percentage of homes that meet the Mortgage rate condition. Fig. 2(c) contains the time series for the percentage of homes that meet both 4.1. The aggregate value of mortgage put options conditions; such homes are candidates for potential cash- out refinancing. It can be seen that there are only a few We measure the value of the guarantee embedded in periods—for example, the early and late 1990s and the each non-recourse mortgage as the value of a put option period between 2001 and 2005—during which a large written on the underlying real estate. Since Merton’s (1977) fraction of homes meets both constraints and for which analysis of deposit insurance, the use of derivatives-pricing the assumed 4.00% refinancing intensity represents the models to value guarantees has become standard. Such an actual likelihood of cash-out refinancing. approach is forward-looking by construction, providing a Based on the goodness-of-fit metrics reported in Table 2 consistent framework for estimating potential losses based and the full time series shown in Fig. 1, we believe that our on current market conditions—in particular, the price and simulation under refinancing rule (2)—where the refinancing volatility of the guaranteed asset—rather than historical intensity is constant through time at the level of 4.00%—is experience. Of course, derivatives-pricing models do require properly calibrated to assess the impact of refinancing on the additional assumptions, e.g., complete markets and a spe- systemic risk of the U.S. residential mortgage market. We cific stochastic process (one that is consistent with com- adopt this specification in our analysis of such risks in pleteness such as geometric Brownian motion). We adopt a Section 4. While this rule implies a uniform probability of discrete-time version of these assumptions in (A10) cash-out refinancing, we have studied two alternative rules in which the refinancing intensity curve is either linearly (A10) Housing-price dynamics can be approximated by a increasing in time or where the refinancing intensity under- discrete-time geometric random walk represented goes a discrete break in 1988 (as motivated by Bennett, by a recombining binomial tree, and markets A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45 37

Fig. 1. A comparison of Total mortgages outstanding and Cumulative equity extractions produced by our simulation and Total mortgage liability series from Flow of Funds Accounts data and the Cumulative equity extractions series of Greenspan and Kennedy (2005). Cash-out refinancing takes place according to the probabilistic rule given in (2), where the Base refinancing rate is 0.1% per month and the refinancing intensity is 4.00%. The data refer to the U.S. residential housing market. (a) Total mortgages outstanding and (b) cumulative equity extractions.

are dynamically complete so options on property Under (A10), we model the guarantee in non-recourse values can be priced by no-arbitrage arguments mortgages as a ‘‘Bermuda’’ put option—an option that can alone. be exercised at certain dates in the future, but only on 38 A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45

100 100

80 80

60 60

constraint 40 40 rate constraint

20 20 Percent of homes meeting the LTV Percent of homes meeting the interest 0 0 1/1/1925 1/1/1934 1/1/1940 1/1/1946 1/1/1955 1/1/1958 1/1/1961 1/1/1964 1/1/1967 1/1/1970 1/1/1976 1/1/1979 1/1/1982 1/1/1985 1/1/1997 1/1/2006 1/1/1997 1/1/1919 1/1/1922 1/1/1928 1/1/1931 1/1/1937 1/1/1943 1/1/1949 1/1/1952 1/1/1973 1/1/1988 1/1/1991 1/1/1994 1/1/2000 1/1/2003 1/1/1919 1/1/1922 1/1/1925 1/1/1928 1/1/1931 1/1/1934 1/1/1937 1/1/1940 1/1/1943 1/1/1946 1/1/1949 1/1/1952 1/1/1955 1/1/1958 1/1/1961 1/1/1964 1/1/1967 1/1/1970 1/1/1973 1/1/1976 1/1/1979 1/1/1982 1/1/1985 1/1/1988 1/1/1991 1/1/1994 1/1/2000 1/1/2003 1/1/2006

100

40 both constraints

Percent of homes meeting 20

0 1/1/1919 1/1/1922 1/1/1925 1/1/1928 1/1/1931 1/1/1934 1/1/1937 1/1/1940 1/1/1943 1/1/1946 1/1/1949 1/1/1952 1/1/1955 1/1/1958 1/1/1961 1/1/1964 1/1/1967 1/1/1970 1/1/1973 1/1/1976 1/1/1979 1/1/1982 1/1/1985 1/1/1988 1/1/1991 1/1/1994 1/1/1997 1/1/2000 1/1/2003 1/1/2006

Fig. 2. Simulated time series of the percentage of homes meeting the (a) LTV condition in (2); (b) the MR condition in (2); (c) both conditions. The results are based on the optimized parameters (see Table 2) with the base refinancing rate set to 0.1% per month and the refinancing intensity equal to 4.00% per month. those fixed dates—and we set these exercise dates to be Fig. 4 shows the simulated time series for the aggre- once a month, just prior to each mortgage payment date.6 gate value of put options for the cases of no-cash-out vs. The exercise price is the amount of the outstanding loan, cash-out refinancing using our calibrated uniform refi- which declines over time due to the monthly mortgage nancing rule, and Table 3 contains the numerical values payments. Before we can implement this option-pricing for each quarter between 2005Q1 and 2008Q4. During model, we must determine the volatility of the underlying normal times, homeowners’ equity absorbs the first losses asset on which the option is written, as well as any from a decline in residential real-estate prices (see Fig. 3). ‘‘dividend yield’’ that may affect the value of that asset. However, the process of equity extraction causes the We set these two parameters to the values reported in size of this buffer to decrease, resulting in a larger portion Table 1. In each run of our simulation, we calculate the of the losses transferred to the equity-holders and debt- value of the put option and various risk metrics related to holders of various mortgage-lending entities (through the the embedded option in each mortage. We then aggregate complex risk redistribution methods shown in the dotted these results to construct a bottom-up estimate of the section of Fig. 3). Our simulations show that with the overall value of the put options and corresponding risk downturn in residential real estate in 2007 and 2008, the exposures in the system. value of the guarantees extended to homeowners by mortgage lenders increased substantially.7 In particular,

6 We use the Cox-Ross-Rubinstein (see Cox and Rubinstein, 1985) binomial tree algorithm to price these options, and implement it in 7 Note that negative correlation between volatility and prices has Matlab (Version 7.2) using the Financial Derivatives Toolbox (Version been documented in several asset classes (see, for example, Bekaert and 4.0) and the functions: crrtimespec, crrsens, crrtree, instopt- Wu, 2000 for the equities case). To the extent that this negative stock, intenvset, and stockspec. See http://www.mathworks.com correlation holds in real-estate markets as well, our volatility for documentation and additional details. parameter—which is an approximate long-term average—is likely to A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45 39

GSE balance sheet

Assets Liabilities

RMBS Debt Government financial Equity guarantee Household real estate balance sheet Asset owners balance sheet

Assets Liabilities Assets Liabilities RMBS Real estate Mortgage RMBS and/or Debt Home equity RMBS CDO Equity

RMBS CDO Banks balance sheet

Assets Liabilities Assets Liabilities

RMBS pool Senior tranche RMBS and/or Debt Mezzanine tranche RMBS CDO Equity Equity

Fig. 3. Residential mortgage-backed security, (RMBS), interlinked balance sheet of entities backed by the underlying real estate, based on Gray, Merton, and Bodie (2008). Intermediate risk redistributions—through, for example, RMBS and collateralized debt obligations (CDOs)—will be ignored in our simulations. by the end of 2008Q4, the total put value of the guarantee which increased to $801.13 million for each 1% drop in embedded in mortgages was $1.7 trillion under the cash- home values by the last quarter of 2008. The size and out refinancing simulation, as compared to $330 billion increase in the gammas of these options indicate substantial under the no-cash-out refinancing simulation. nonlinearity in the risk of the mortgage system that may need to be accounted for in systemic risk measurement and analysis. Table 3 contains delta and gamma estimates for 4.2. U.S. mortgage system delta, gamma, and vega simulations without cash-out refinancing as well. Another aspect of risk in the mortgage system can be The overall level of risk in the mortgage system can be measured by estimating the sensitivity of the value of calculated based on the sensitivities of the value of mort- embedded options to an increase in home price volatility, gages’ embedded put options to changes in the level or also known as the option’s ‘‘vega.’’ Based on our calculations, volatility of home prices. While the exact value of these risk we estimate that the total value of the embedded put options metrics depends on the particular model used for option in non-recourse mortgages would increase by approximately pricing, the nature of risk in the mortgage system trans- $70–$80 billion for each 1% increase in home price volatility cends the specifics of the models. For example, regardless of in the years leading up to the crisis. While Fig. 5 shows a the exact model, the value of the guarantees increases as the largeincreaseinvegaovertime,duringtherecentcrisisthis value of the collateral declines. Using the language of option measure of risk first increased and then declined. Portfolios pricing,thedeltaofthemortgageguaranteesispositive. of options can exhibit such counterintuitive behavior because Furthermore, the rate of the increase is itself increasing, or of the nonlinearity of these metrics. For example, in the in the option language, the gamma is positive. Black-Scholes model, the vega of options way in or out of the Fig. 5 and Table 3 report these metrics for the simulation money is low, but is quite high for options near the money. based on the uniform refinancing rule (we provide these These nonlinearities can give rise to the effects shown here metrics for alternative refinancing rules in the Appendix). for the U.S. mortgage system. As reported in Table 3, in the first quarter of 2005, we estimate that the aggregate value of all embedded put 4.3. Sensitivity to model parameters and the refinancing rule options would increase by $18.17 billion for each 1% drop in home prices. By the last quarter of 2008, this sensitivity The accuracy of the simulation results of Sections 4.1 almost doubled to $38.13 billion for each 1% drop in home and 4.2 depends, of course, on the values of the various values. This large increase is due to the large gamma of parameters of our simulations, as well as the assumed these embedded options, as reported in Table 3.Forthe form of the behavioral refinancing intensity function. same simulation, the estimated gamma was $573.79 million We have conducted a series of sensitivity analyses that per1%dropinhomevaluesinthefirstquarterof2005, we will summarize in this section. We first consider the estimates for the aggregate value of the put options in non-recourse mortgage loans under (footnote continued) underestimate the realized volatility during a market downturn, which, the two alternative refinancing rules. As reported in in turn, will underestimate aggregate losses. Table 4, the results are remarkably stable across different 40 A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45

Total put values 1,800

Total put value under calibrated uniform refinancing rule Total put value under no refinancing 1,440

1,080

720 Total put values ($B)

360

0 1/1/2006 1/1/1919 1/1/1922 1/1/1925 1/1/1928 1/1/1931 1/1/1934 1/1/1937 1/1/1940 1/1/1943 1/1/1946 1/1/1949 1/1/1952 1/1/1955 1/1/1958 1/1/1961 1/1/1964 1/1/1967 1/1/1970 1/1/1973 1/1/1976 1/1/1979 1/1/1982 1/1/1985 1/1/1988 1/1/1991 1/1/1994 1/1/1997 1/1/2000 1/1/2003

Fig. 4. Simulated time series of the aggregate value of total guarantees extended to U.S. homeowners by mortgage lenders for cash-out and no-cash-out refinancing scenarios. For the cash-out refinancing case, refinancing takes place according to probabilistic rule (2) in which the base refinancing rate is 0.1% per month and the Refinancing intensity is constant over time and equal to 4.00%.

Table 3 Simulated time series of the aggregate value and sensitivities of total guarantees extended to homeowners by mortgage lenders for cash-out and no- cash-out refinancing scenarios for each quarter from 2005Q1 to 2008Q4 (put values are in $billions, deltas are in $billions per 1% decline in home prices, gammas are in $millions per 1% decline in home prices, and vegas are in $billions per 1% increase in home price volatility). For the cash-out refinancing case, refinancing takes place according to probabilistic rule (2) in which the base refinancing rate is 0.1% per month and the refinancing intensity is constant over time and equal to 4.00%.

No cash-out Cash-out

Date Put value Delta Gamma Vega Put value Delta Gamma Vega

Mar-05 64.90 2.24 79.32 10.67 566.60 18.17 573.79 74.64 Jun-05 65.70 2.27 80.11 10.84 568.80 18.30 580.83 76.22 Sep-05 69.20 2.37 82.70 11.18 592.30 18.93 598.38 78.24 Dec-05 74.20 2.51 86.67 11.62 601.30 19.26 610.92 79.73 Mar-06 81.50 2.70 91.48 12.09 621.10 19.79 624.81 80.87 Jun-06 87.10 2.87 96.71 12.55 611.70 19.72 630.83 80.94 Sep-06 100.90 3.23 105.41 13.36 644.90 20.52 647.87 81.94 Dec-06 114.90 3.57 113.41 14.06 698.70 21.77 673.15 83.48 Mar-07 126.80 3.86 120.11 14.55 748.40 22.90 695.70 84.39 Jun-07 137.30 4.14 127.12 15.08 782.80 23.74 715.13 85.05 Sep-07 153.30 4.52 135.97 15.72 831.20 24.81 735.34 85.44 Dec-07 178.90 5.05 145.70 16.14 951.00 27.14 770.51 85.57 Mar-08 221.80 5.82 155.67 16.21 1185.10 31.18 812.91 84.18 Jun-08 252.40 6.35 161.10 16.12 1345.20 33.70 829.32 81.74 Sep-08 278.40 6.76 164.30 16.10 1465.40 35.24 823.54 78.97 Dec-08 330.20 7.42 164.96 15.62 1727.20 38.13 801.13 73.75

reﬁnancing rules. This stability is likely due to the fact performed additional simulations for rent yields of 3% that each of these rules is calibrated to match the overall and 5%, and home price volatilities of 6% and 10%. To size and growth in the U.S. residential mortgage system conserve space, we have reported only the resulting by matching our two reference series (see the Appendix). estimates for the total put value under these parameter To gauge the sensitivity of our simulations to the values in Table 5. These results show that in the fourth rent yield and home price volatility assumptions, we quarter A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45 41

Option sensitivity - Delta Option sensitivity - Gamma 40 900 Total mortgage delta under calibrated uniform refinancing rule Total mortgage gamma under calibrated uniform refinancing rule Total mortgage delta under no refinancing Total mortgage gamma under no refinancing

32 720

24 540

16 360 in home values) drop in home values) 8 180 Total put gamma ($M per 1-percent Total put delta ($B per 1-percent drop 0 0 1/1/1919 1/1/1922 1/1/1925 1/1/1928 1/1/1931 1/1/1934 1/1/1937 1/1/1940 1/1/1943 1/1/1946 1/1/1949 1/1/1952 1/1/1955 1/1/1958 1/1/1961 1/1/1964 1/1/1967 1/1/1970 1/1/1973 1/1/1976 1/1/1979 1/1/1982 1/1/1985 1/1/1988 1/1/1991 1/1/1994 1/1/1997 1/1/2000 1/1/2003 1/1/2006 1/1/1919 1/1/1922 1/1/1925 1/1/1928 1/1/1931 1/1/1934 1/1/1937 1/1/1940 1/1/1943 1/1/1946 1/1/1949 1/1/1952 1/1/1955 1/1/1958 1/1/1961 1/1/1964 1/1/1967 1/1/1970 1/1/1973 1/1/1976 1/1/1979 1/1/1982 1/1/1985 1/1/1988 1/1/1991 1/1/1994 1/1/1997 1/1/2000 1/1/2003 1/1/2006

Option sensitivity - Vega 90 Total mortgage vega under calibrated uniform refinancing rule Total mortgage vega under no refinancing 72

18 increase in home price volatility) Total put vega ($B per 1-percent

0 1/1/1934 1/1/1919 1/1/1922 1/1/1925 1/1/1928 1/1/1931 1/1/1937 1/1/1940 1/1/1943 1/1/1946 1/1/1949 1/1/1952 1/1/1955 1/1/1958 1/1/1961 1/1/1964 1/1/1967 1/1/1970 1/1/1973 1/1/1976 1/1/1979 1/1/1982 1/1/1988 1/1/1991 1/1/1994 1/1/1997 1/1/2000 1/1/2003 1/1/2006 1/1/1985

Fig. 5. Simulated time series of the sensitivities of the aggregate value of total guarantees extended to homeowners by mortgage lenders for cash-out and no-cash-out refinancing scenarios. Panel (a) plots the sensitivity to a 1% drop in home prices, Panel (b) plots the rate of change of (a) with respect to home prices, and Panel (c) plots the sensitivity to a 1% increase in home price volatility. For the cash-out refinancing case, refinancing takes place according to probabilistic rule (2) in which the base refinancing rate is 0.1% per month and the refinancing intensity is constant over time and equal to 4.00%.

Table 4 Simulated time series of the aggregate value and sensitivities of total guarantees extended to homeowners by mortgage lenders for cash-out and no-cash-out reﬁnancing scenarios for each quarter from 2005Q1 to 2008Q4 (put values are in $billions, deltas are in $billions per 1% decline in home prices, gammas are in $millions per 1% decline in home prices, and vegas are in $billions per 1% increase in home price volatility) for three reﬁnancing rules: Uniform (4.00%), Linear (4.50%), Uniform with break (3.75% before 1988; 4.25% from 1988 onward). See Table 2, Tables A.4 and A.5 of the Appendix for details on how these rules are calibrated.

Uniform (base case) Linear Uniform with break

Date Put value Delta Gamma Vega Put value Delta Gamma Vega Put value Delta Gamma Vega

Mar-05 566.60 18.18 573.79 74.64 578.10 18.45 578.63 75.21 588.30 18.82 591.95 76.94 Jun-05 568.60 18.30 580.83 76.22 578.80 18.56 586.04 76.82 586.20 18.85 597.22 78.33 Sep-05 592.30 18.93 598.38 78.24 603.10 19.21 603.99 78.94 610.90 19.49 614.44 80.39 Dec-05 601.30 19.26 610.92 79.73 612.10 19.55 617.21 80.52 617.80 19.78 626.14 81.79 Mar-06 621.10 19.79 624.81 80.87 631.20 20.06 631.21 81.64 636.60 20.27 638.94 82.84 Jun-06 611.70 19.72 630.83 80.94 621.40 19.99 637.12 81.71 626.90 20.20 644.63 82.86 Sep-06 644.90 20.53 647.87 81.94 654.60 20.80 654.33 82.82 659.10 20.99 661.77 83.87 Dec-06 698.70 21.78 673.15 83.49 707.90 22.04 678.76 84.26 712.20 22.21 685.50 85.24 Mar-07 748.40 22.90 695.70 84.39 756.70 23.13 699.87 85.01 761.40 23.31 707.30 86.05 Jun-07 782.80 23.75 715.13 85.05 789.30 23.92 717.79 85.53 793.60 24.11 726.16 86.62 Sep-07 831.20 24.81 735.34 85.44 837.90 24.99 737.92 85.86 842.60 25.19 745.96 86.96 Dec-07 951.00 27.15 770.51 85.57 955.80 27.24 770.24 85.76 961.80 27.50 780.43 86.96 Mar-08 1185.10 31.19 812.91 84.18 1190.90 31.27 812.12 84.27 1196.60 31.54 822.13 85.48 Jun-08 1345.20 33.71 829.32 81.74 1352.70 33.79 827.43 81.77 1358.50 34.08 838.22 82.97 Sep-08 1465.40 35.24 823.54 78.97 1472.30 35.30 821.47 78.97 1478.70 35.61 832.92 80.09 Dec-08 1727.20 38.14 801.13 73.75 1733.70 38.16 797.50 73.65 1742.90 38.54 811.56 74.71 42 A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45

Table 5 Simulated total value of guarantees extended to homeowners by mortgage lenders (in $billions) for various values of home price volatility (Vol) and rent yield (RY) under the Uniform (4%) reﬁnancing rule from 2005Q1 to 2008Q4.

Vol¼6% Vol¼8% Vol¼10%

Date RY¼3% RY¼4% RY¼5% RY¼3% RY¼4% RY¼5% RY¼3% RY¼4% RY¼5%

Mar-05 225.00 430.60 729.30 346.70 566.60 859.50 489.30 719.60 1007.40 Jun-05 223.60 430.40 732.30 346.40 568.60 866.20 491.10 725.10 1018.70 Sep-05 236.10 450.90 762.10 362.50 592.30 899.00 511.50 753.10 1056.00 Dec-05 239.90 457.30 772.70 368.30 601.30 912.50 519.90 765.20 1073.00 Mar-06 252.70 475.30 795.90 383.40 621.10 937.50 537.60 787.40 1100.10 Jun-06 248.20 465.90 781.20 378.00 611.70 923.90 531.70 778.20 1087.80 Sep-06 270.80 497.30 820.60 403.90 644.90 963.90 560.70 813.40 1128.80 Dec-06 307.20 548.30 885.30 445.60 698.70 1029.30 607.40 870.30 1195.50 Mar-07 343.20 596.40 943.60 485.60 748.40 1087.30 651.10 921.80 1253.80 Jun-07 369.00 629.70 982.90 514.20 782.80 1126.50 682.30 957.60 1293.40 Sep-07 407.20 677.40 1038.00 555.10 831.20 1180.80 725.60 1006.70 1347.10 Dec-07 504.90 797.50 1175.40 657.20 951.00 1314.80 831.80 1126.80 1478.50 Mar-08 706.50 1035.40 1440.00 862.20 1185.10 1571.40 1040.40 1358.40 1728.00 Jun-08 858.70 1200.90 1612.60 1012.00 1345.20 1737.30 1188.30 1513.70 1887.60 Sep-08 981.20 1326.80 1737.70 1129.90 1465.40 1856.80 1301.80 1628.50 2001.40 Dec-08 1241.20 1599.20 2014.40 1381.60 1727.20 2122.60 1545.80 1880.00 2256.00

of 2008, the simulated loss estimates range from a low 5.1. Heuristic vs. general-equilibrium analysis of $1241 billion (3% rent yield, 6% volatility) to a high of $2256 billion (5% rent yield, 10% volatility). As volatility Our simulations are based on a number of simplifying increases, or as the rent yield increases, ceteris paribus, assumptions. While we have attempted to err on the side the embedded guarantee becomes more valuable. While of lower implied losses whenever possible, some assump- rent yields may be relatively stable over time, it can be tions may have the opposite effect, e.g., assuming that all argued that home price volatility is more variable. mortgages are non-recourse loans. Incorporating more In particular, as the national home price index reached realistic features of the housing market such as its peak in June 2006 and began to decline, home price adjustable-rate and negative-amortization mortgages volatility is likely to have increased significantly beyond with teaser rates, NINJA loans, and regional differences historical levels, which implies that our estimates for the in the U.S. residential real-estate market, bankruptcy aggregate put value may underestimate actual losses. laws, and homeowner asset and income dynamics, may Tables A.6–A.8 in the Appendix provide similar sensitivity increase the accuracy of the simulation. analyses for the estimated delta, gamma, and vega mea- However, our analysis is not designed to capture sures for the aggregate put. We have conducted a number feedback effects among all endogenous variables such as of other sensitivity analyses but due to space limitations, home prices, interest rates, household income, and bor- the results are provided in the Appendix. Overall, we have rowing and lending behavior. Therefore, standard found the magnitudes of the results to be remarkably comparative-statics questions, such as ‘‘How much would robust to variations in assumptions and parameters. home prices have risen if the Fed had not cut interest As noted earlier, this stability is likely due to the fact that rates from 2000 to 2003?’’, are not addressed in our each of these rules is calibrated to match the overall size simulations. Instead, our narrower reduced-form focus and growth of the U.S. residential mortgage system as has been to gauge the magnitude of the refinancing captured by our two reference series. ratchet effect on mortgage lenders. A more formal general- equilibrium analysis of these markets would begin with optimizing households from which the demand for housing and mortgages are derived, aggregated, and equilibrated 5. Discussion with optimizing home builders and mortgage lenders that supply the homes and mortgages, respectively, to house- In this section, we present a number of qualifications, holds. While computable general-equilibrium models have extensions, and implications of our simulation of the U.S. become considerably more sophisticated in recent years (see, residential housing market. In Section 5.1,wecontrastthe for example, Dixon and Rimmer, 2002), the dynamic and heuristic nature of our simulations to traditional general- stochastic nature of the demand and supply decisions are equilibrium analysis. We acknowledge in Section 5.2 that sufficiently complex—even for a single agent—that con- we have not modeled the behavior of lenders in our structing a true stochastic dynamic general-equilibrium simulations. We distinguish between market risk and sys- model of the entire U.S. housing market seems computa- temic risk in Section 5.3.InSection 5.4 we observe that the tionally impractical. Nevertheless, some useful insights may welfare implications of the recent financial crisis, and the be gleaned from considering special cases of such optimiz- events leading up to it, are not yet fully understood. ing behavior and equilibrium, e.g., Pliska (2006), Fortin, A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45 43

Michelson, Smith, and Weaver (2007),andAgarwal, comparable trends in real interest rates. In a country where Driscoll, and Laibson (2008), which may be worth pursuing cash-out refinancing is easier or more common—perhaps further. because of familiarity or other social characteristics—alarger portion of the increase in homeowner’s equity is extracted by 5.2. Lending behavior the owner. This would, in turn, cause more synchronization in homeowners’ leverage and more severe losses for lenders Any analysis of the Financial Crisis of 2007–2009 in the wake of home-price declines. would not be complete without some discussion of the More importantly, the main thrust of our analysis is behavior of mortgage lenders and associated businesses. that the refinancing ratchet effect is a wholly separate Our simulations assume that all household demand for mechanism that operates irrespective of the supply of mortgages and refinancing is satisfied at prevailing his- credit, and one that must be considered a potential source torical rates, i.e., the supply of funds to borrowers is of systemic risk in its own right. infinitely elastic at all times. While this may have been a reasonable approximation to reality during the decade 5.3. Market risk vs. systemic risk prior to the peak of the housing market in 2006, our motivation for this simplifying assumption is to gauge the While the $1.7 trillion figure seems imposing, large impact of the refinancing ratchet effect in isolation. financial losses do not necessarily imply significant sys- However, supply shocks certainly must have had an temic risk. For example, on April 14, 2000, the Center for impact on systemic risk in recent years as well. Therefore, Research in Security Prices (CRSP) value-weighted stock an important open question is how lenders behaved market index (excluding dividends) declined by 6.63%, during the course of our simulations, and what economic implying an aggregate one-day loss of approximately or behavioral forces led them to engage in such behavior. $1.04 trillion to corporate America. While certainly unfor- A tractable and empirically plausible model of lending tunate, this event was not particularly memorable, nor behavior is beyond the scope of our current simulation, was it a cause for national alarm or emergency govern- and it deserves a separate set of simulation studies in its ment intervention. Market risk is distinct from systemic own right (one possible starting point is Thurner, Farmer, risk; the latter arises when large financial losses affect and Geanakoplos, 2009). However, it is not difficult to important economic entities that are unprepared for and speculate about the factors those simulations might unable to withstand such losses, causing a cascade of include. In addition to modeling the behavior of banks, failures and widespread loss of confidence. This element which are the traditional sources of home loans, such a of surprise lies at the heart of the recent financial crisis. simulation must also account for a host of financial The fact that the three conditions that cause the refinan- innovations that have emerged only recently, including cing ratchet effect—rising home prices, falling interest securitized debt (e.g., CDOs and CDO-squareds), credit rates, and easy access to refinancing opportunities—are default swaps and related insurance products, Internet- individually innocuous and are often viewed as signs of based marketing of consumer-finance products, the economic growth and prosperity creates the element of growth of the ‘‘shadow banking industry’’ and illiquidity, surprise. Therefore, not only is the magnitude of losses and the globalization of financial markets. Rajan (2006), caused by the refinancing ratchet effect large, but these Gorton (2008, 2009), Brunnermeier (2009), and Gorton losses are also more likely to be unexpected, resulting in and Metrick (2012) provide overviews of some of these systemic risk to the financial system. developments. In addition, these simulations must incorporate the impact of rating agencies, GSEs, and broader 5.4. Welfare implications government policies in promoting cheap financing for would-be homeowners, as well as the increasing compe- Although much has already been written about the tition for yield among asset-managers and asset-owners. Financial Crisis of 2007–2009, its welfare implications for Collectively, these developments contributed to the enor- homeowners, lenders, and intermediaries are not yet fully mous supply of funds available to homeowners during the understood. While many homeowners have been adversely past decade, but further analysis is needed before we can affected by rising interest rates, foreclosures, and falling determine the relative importance of each. property values, there are other satisfied and solvent home- The challenge in constructing a simulation with all of owners who are homeowners only because of the business these features is the fact that there is precious little history practices, government policies, and economic circumstances on which to calibrate many of the parameters. In contrast to that contributed to the refinancing ratchet effect. Eliminat- typical simulations that assume a statistically stationary ing or otherwise restricting these business practices and environment, simulating the supply of funds for residential policies may benefit some groups, but it will no doubt real-estate purchases involves the historically unique finan- disadvantage others. Moreover, as discussed above, we have cial innovations described above. This simulation may pro- not attempted to model the supply side of the refinancing vide a clue as to the magnitude of the current crisis, as well industry, which no doubt contributed to the growth of as its apparent uniqueness in recent history. The mechanism home prices, leverage ratios, and systemic risk. Many have discussed in this paper is surely relevant when comparing criticized the role of securitization, insurance, and financial the impact of housing-price crashes across countries. innovation in creating the crisis, but during the decade As discussed in Hubbard and Mayer (2009), many countries leading up to the peak of the housing market in 2006, these experienced similar housing-price growth driven by developments were responsible for the low-interest-rate 44 A.E. Khandani et al. / Journal of Financial Economics 108 (2013) 29–45 and easy-credit environment that was so conducive to growth, capital inflows, and financial liberalization and global economic growth and the ‘‘ownership society.’’ Any innovation. Successfully managing systemic risk will policy recommendations with respect to the Financial Crisis require flexible, creative, and well-trained professionals of 2007–2009 must balance these myriad trade-offs between who understand the fundamental drivers of such risk, not individual and institutional stakeholders. static rules meant to prevent history from repeating.

6. Conclusion Appendix A. Supplementary data During periods of rising home prices, falling interest rates, and increasingly competitive and efficient refinan- Supplementary data associated with this article can be cing markets, cash-out refinancing is like a ratchet, found in the online version at http://dx.doi.org/10.1016/j. incrementally increasing homeowner leverage as real- jfineco.2012.10.007. estate values appreciate without the ability to symme- trically decrease leverage by increments as real-estate values decline. Using a numerical simulation calibrated to References the basic time-series properties of the U.S. residential housing market, we show that this ratchet effect is Agarwal, S., Driscoll, J., Laibson, D., 2008. Optimal mortgage refinancing: capable of generating the magnitude of losses suffered a closed form solution. NBER Working Paper No. w13487. by mortgage lenders during the Financial Crisis of Archer, W., Ling, D., McGill, G., 1997. 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